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      <div class="title">
        NeurIPS 2024 SPOTLIGHT
      </div>
      <div class="title">
        3D Gaussian Splatting as Markov Chain Monte Carlo
      </div>

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            <div class="is-size-5 publication-authors">
              <span class="author-block">
                <a href="https://shakibakh.github.io/">Shakiba Kheradmand</a
                ><sup>1</sup>,</span
              >
              <span class="author-block">
                <a href="http://drebain.com/"> Daniel Rebain</a
                ><sup>1</sup>,</span
              >
              <span class="author-block">
                <a href="https://hippogriff.github.io/"> Gopal Sharma</a
                ><sup>1</sup>,</span
              >
              <span class="author-block">
                <a href="https://wsunid.github.io/"> Weiwei Sun</a
                ><sup>1</sup>,</span
              >
              <br />
              <span class="author-block">
                <a href="https://scholar.google.com/citations?user=1iJfq7YAAAAJ&hl=en"> Yang-Che Tseng</a
                ><sup>1</sup>,</span
              >
              <span class="author-block">
                <a href="http://www.hossamisack.com/">Hossam Isack</a
                ><sup>2</sup>,
              </span>
              <span class="author-block">
                <a href="https://abhishekkar.info/">Abhishek Kar</a><sup>2</sup>
              </span>
              <br />
              <span class="author-block">
                <a href="https://taiya.github.io/">Andrea Tagliasacchi</a
                ><sup>3, 4, 5</sup>
              </span>
              <span class="author-block">
                <a href="https://www.cs.ubc.ca/~kmyi/">Kwang Moo Yi</a
                ><sup>1</sup>
              </span>
            </div>

            <div class="is-size-5 publication-authors">
              <span class="author-block"
                ><sup>1</sup>University of British Columbia</span
              >
              <span class="author-block"><sup>2</sup>Google Research</span>
              <span class="author-block"><sup>3</sup>Google DeepMind</span>
              <br />
              <span class="author-block"
                ><sup>4</sup>Simon Fraser University</span
              >
              <span class="author-block"
                ><sup>5</sup>University of Toronto</span
              >
            </div>
          </div>
        </div>
      </div>

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              <span>Paper</span>
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            <a href="https://arxiv.org/abs/2404.09591" class="external-link button is-normal is-rounded is-dark">
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              <span>arXiv</span>
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            <a
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              <span>Video</span>
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            <a
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        <hr />
      </div>

      <div class="parent-video-compare-container" id="trainb">
        <div class="video-compare-container" id="materialsDiv">
          <video
            class="video"
            id="materials"
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            playsinline
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            src="./resources/training_rand_compare/bicycle_both-rand.mp4"
            onplay="resizeAndPlay(this)"
          ></video>
          <canvas height="0" class="videoMerge" id="materialsMerge"></canvas>
        </div>
        <br>
        <p class="justified">
          Novel view reconstructions for <strong>(right) our method</strong>
          and <strong>(left) conventional</strong> 3D Gaussian Splatting with
          random initializations. Our method, even with random initialization,
          faithfully reconstructs the scene (e.g.. buildings at the back and
          the ground texture) providing much higher quality renderings.
        </p>
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        <hr />
      </div>

      <h1>Abstract</h1>
      <div class="parent-video-compare-container">
        <p class="justified">
          While 3D Gaussian Splatting has recently become popular for neural
          rendering, current methods rely on carefully engineered cloning and
          splitting strategies for placing Gaussians, which can lead to
          poor-quality renderings, and reliance on a good initialization. In
          this work, we rethink the set of 3D Gaussians as a random sample
          drawn from an underlying probability distribution describing the
          physical representation of the scene---in other words, Markov Chain
          Monte Carlo (MCMC) samples. Under this view, we show that the 3D
          Gaussian updates can be converted as Stochastic Gradient Langevin
          Dynamics (SGLD) update by simply introducing noise. We then rewrite
          the densification and pruning strategies in 3D Gaussian Splatting as
          simply a deterministic state transition of MCMC samples, removing
          these heuristics from the framework. To do so, we revise the
          `cloning' of Gaussians into a relocalization scheme that
          approximately preserves sample probability. To encourage efficient
          use of Gaussians, we introduce a regularizer that promotes the
          removal of unused Gaussians. On various standard evaluation scenes,
          we show that our method provides improved rendering quality, easy
          control over the number of Gaussians, and robustness to
          initialization.
        </p>
      </div>

      <div class="parent-video-compare-container">
        <hr />
      </div>

      <h1>More Results</h1>

      <div class="parent-video-compare-container">
        <table class="tbl_video" style="width:100%;"">
        <tr>
          <td colspan="4" style="background-color: #d1c4ce; font-size: 20px">
            '10' sequence from OMMO dataset
          </td>
        </tr>
        <tr>
          <td width="50%" style="font-size: 18px">3DGS-Random</td>
          <td width="50%" style="font-size: 18px">3DGS</td>
        </tr>
        <tr>
          <td colspan="2">
            <video
              class="kitti360"
              id="00"
              width="95%"
              preload="auto"
              playsinline
              webkit-playsinline
              loop
              autoplay
              muted
            >
              <source src="resources/10/10.mp4" type="video/mp4" />
            </video>
          </td>
        </tr>
        <tr>
          <td width="50%" style="font-size: 18px">Ours-Random</td>
          <td width="50%" style="font-size: 18px">Ours</td>
        </tr>

        <table class="tbl_video" style="width:100%;"">
        <tr>
          <td colspan="4" style="background-color: #d1c4ce; font-size: 20px">
            'Stump' sequence from the MipNeRF360 dataset (pay attention to the
            details between the leaves)
          </td>
        </tr>
        <tr>
          <td width="50%" style="font-size: 18px">3DGS-Random</td>
          <td width="50%" style="font-size: 18px">3DGS</td>
        </tr>
        <tr>
          <td colspan="2">
            <video
              class="kitti360"
              id="00"
              width="95%"
              preload="auto"
              playsinline
              webkit-playsinline
              loop
              autoplay
              muted
            >
              <source src="resources/stump/stump.mp4" type="video/mp4" />
            </video>
          </td>
        </tr>
        <tr>
          <td width="50%" style="font-size: 18px">Ours-Random</td>
          <td width="50%" style="font-size: 18px">Ours</td>
        </tr>
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